Time: 14:00-15:00, Monday, October 28 2024

Venue: E4-233, Yungu Campus

Zoom ID: 916 8484 3713

Passcode: 176002

Speaker: Shouhong Wang, Indiana University Bloomington

Title: Dynamical Transitions in Fluid Flows

Abstract: The first part of the talk is to introduce the general framework of phase transition dynamics deterministic systems, with various applications to fluid flows. This is based on joint work with Dr. Tian Ma.

In the second part of the talk, we study transitions in stochastic non-equilibrium systems.

As we know, a central challenge in physics is to describe non-equilibrium systems driven by randomness. For deterministic systems, the center manifold theory has shown a prodigious efficiency to often completely characterize how the onset of linear instability translates into the emergence of nonlinear patterns, associated with genuine physical regimes. In presence of random fluctuations, the underlying reduction principle to the center manifold is seriously challenged due to large excursions caused by the noise. In this study, we present an alternative framework to cope with these difficulties exploiting the approximation theory of stochastic invariant manifolds, on one hand, and energy estimates measuring the defect of parameterization of the high-modes, on the other. As a result, the approach enables us to predict, from reduced equations of the stochastic fluid problem, the occurrence in large probability of a stochastic analogue to the pitchfork bifurcation, as long as the noise’s intensity and the eigenvalue’s magnitude of the mildly unstable mode scale accordingly. This is joint work with Mickael Chekroun, Honghu Liu, and James McWilliams [JDE, 346(2023), 145-204].